A confectioner has 300 pounds of a chocolate that is 1 part cocoa butter to 7 parts caramel. How much chocolate that is 1 part cocoa butter to 15 parts caramel should be combined with the first in order to create a new chocolate that is 1 part cocoa butter to 9 parts caramel? pls help???!!!!!
Add up the amounts of cocoa:
(1/8)(300) + (1/16)x = (1/10)(300+x)
x = 200
If the fractions seem confusing, note that the 1:7 ratio means there are 8 parts of ingredient, only 1 of which is cocoa.
The question:A confectioner has 300 pounds of a chocolate that is 1 part cocoa butter to 7 parts caramel. How much chocolate that is 1 part cocoa butter to 15 parts caramel should be combined with the first in order to create a new chocolate that is 1 part cocoa butter to 9 parts caramel?
The answer: 200 pounds. (this is correct, I used an answering machine, double checked all answers and asked an expert)
its correct
200 pounds
To solve this problem, we can use a weighted average approach. Let's break it down step by step:
Step 1: Calculate the ratio of cocoa butter to caramel in the original chocolate.
The original chocolate has a ratio of 1 part cocoa butter to 7 parts caramel. This means that for every 1 pound of cocoa butter, there are 7 pounds of caramel.
Step 2: Calculate the ratio of cocoa butter to caramel in the new chocolate.
The desired ratio for the new chocolate is 1 part cocoa butter to 9 parts caramel. This means that for every 1 pound of cocoa butter, there will be 9 pounds of caramel.
Step 3: Calculate the total weight of cocoa butter and caramel in the final chocolate.
Let's assume that x pounds of the new chocolate is combined with the original chocolate. Since the ratio of cocoa butter to caramel in the original chocolate remains the same, the amount of cocoa butter remains unchanged at 1 part (x pounds) in the combined mixture.
The ratio of caramel in the new chocolate is 15 parts, which means there will be 15x pounds of caramel in the combined mixture.
Therefore, the total weight of the combined mixture will be x pounds of cocoa butter and (15x + 300) pounds of caramel.
Step 4: Set up an equation based on the desired ratio.
The desired ratio for the new chocolate is 1 part cocoa butter to 9 parts caramel. Using the information from step 3, we can set up the following equation:
1 / 9 = x / (15x + 300)
Step 5: Solve the equation.
To solve the equation, we can cross-multiply:
9x = 1 * (15x + 300)
9x = 15x + 300
Simplifying the equation:
6x = 300
x = 50
So, 50 pounds of the chocolate that is 1 part cocoa butter to 15 parts caramel should be combined with the original 300 pounds of chocolate to create a new chocolate that is 1 part cocoa butter to 9 parts caramel.
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